Experiment 2: Results and Discussion

The goal of this experiment was to learn the lateral and longitudinal dynamics. The estimated coefficients were then compared against those measured coefficients for the entire test flight. These measured parameters were calculated using the data obtained from the navigation solution which was used by the Brumby MkIII flight controller [32]. In addition, prior to using the data a compatibility check was performed with kinematic analysis [35]. This ensured the data used for training and testing are consistent and error free. The following subsection details the results obtained.

800 805 810 815 820 825

800 805 810 815 820 825

0 0.02 0.04

C y

800 805 810 815 820 825

−0.4

−0.35

−0.3

−0.25

C z

800 805 810 815 820 825

−10

800 805 810 815 820 825

−1

800 805 810 815 820 825

−10

Figure 5.11: Local and global GP estimated (solid blue), global GP estimated (dash-dot green) and measured (dash red) non-dimensional aerodynamic coefficients with prediction uncertainties for the combined approximation (gray) for the Brumby MkIII test Flight 2.

Table 5.4: Experiment 2 coefficient estimation errors.

% Error C_X C_Y C_Z C_l C_m C_n

Flight 4 19.195 23.278 18.365 23.364 22.265 28.173 Flight 5 20.792 24.733 19.925 28.432 19.891 23.714 Flight 6 17.127 19.847 15.174 24.691 17.730 26.245

Estimated Aerodynamic Coefficients

For the complete duration of the flights both lateral and longitudinal parameters were identified. The estimated coefficients and the prediction uncertainties for a segment of test Flight 4 are shown in Figure 5.11. It also shows the estimates by only using the approximated global GP. This is to demonstrate the benefit of utilizing a combined approximation. What is captured by the additional layer of local GP can be seen.

The approximated global GP is a much slower moving function and does not capture the fast variations in data. The additional layer of non-stationary covariance function compensated for this gap.

The relative errors on the estimated parameters were calculated by comparing against the measured. The results are presented in Table 5.4 for all the flights. It was found that the median error on the force coefficients is ±19.83% and on the moment coefficients is ±23.83% of the measured. This is comparable to the estimates from the full DGP (see Table 5.2). The error is contributed to by wing gust (8 - 15 kts) and propagated errors from sensor noise. The coarsely known mass and inertia properties of the platform and any unmodeled characteristics are also captured in the response.

It is also observed that moment coefficients contained the most error. This could be minimized by designing specific flight test maneuvers to excite those dynamics.

In addition to the predictions made the associated uncertainty can provide a notion of confidence on the estimates. In some instances even in the regions of high uncer-tainty the estimates are fairly close to the measured. This is due to the dependency learned between parameters from the global approximate. Likewise if there is less cross coupling between outputs inference through global GP would approach zero

and the predictions would be primarily made using the local model. This flexibility enabled the model to be valid for a large spectrum of the flight envelope. In summary, the model parameters identified from the training flight was proved to be valid for the entire test flight.

5.6 Summary and Conclusion

This chapter demonstrated the use of Gaussian processes to learn aerodynamic co-efficients to model UAV flight dynamics. It was demonstrated through training and extensive testing with real flight data from the Brumby MkIII UAV. The results con-firmed that it is possible to use this technique to construct an accurate model for a UAV. These models are more informative and this approach can reduce long-term costs in flight testing. In particular it is useful when identifying parameters for a UAV with high level of cross coupling such as a platform with a delta wing or an oblique wing. In addition, it was verified that DGP models can handle wind gusts experienced in real flight scenarios.

Apart from estimating accurate parameters and model robustness for unmodeled disturbances, the next most useful outcome of the proposed approach is the estimates of uncertainty of the predictions. These can be used as a verification measure to validate the model’s usefulness. Lack of confidence in the model predictions can serve as the grounds to learn from new information.

Next, it was demonstrated that flight models can be constructed at a much lower com-putational cost while retaining the properties that were gained using the full DGP.

In the approximation model, the global GP captures dependencies between outputs, identifies any coupling between parameters and the local GP captures any correla-tions within those parameters. Finally, the prediccorrela-tions are made with an associated uncertainty which gives a notion of confidence on the learned parameters. Hence, the proposed method can bring forth a more informative flight model that can capture a wide range of the dynamics. The consistency in predictions across various maneuvers confirmed that the parameters learned were a accurate representation of the system.

By having the ability to learn with large flight data sets, it can capture wide range of properties in the data.

Conclusions

This thesis set out to investigate new ways of addressing fundamental challenges in the area of UAV system identification.

System identification for a UAV involves flight testing to collect observation data in order to accurately model the flight dynamics. These models map the platform’s control inputs to its dynamic response. They can be used in modern flight con-troller design, simulator development and to understand the UAV handling qualities.

Previous work has been done on developing models using both parametric and non-parametric approaches. The existing non-parametric approaches require a model structure to regress the observations. This may only be partially known and in some instances may not be available a priori. One example of this is developing a model for a new UAV platform without any prior empirical data from an aircraft catalogue such as the DATCOM [21]. In such cases, the modeling process is labor intensive and re-quires coarse approximations to be made. A limited model structure will restrict its applicability to a narrow band of the flight envelope. Such restrictions can be alleviated by using a non-parametric system identification technique. However, the existing approaches are either limited to operating only within a trained trajectory or do not provide a complete representation of the system.

Another primary challenge in parameter identification is when a model is to be learned that has a high level of cross-coupling between the longitudinal and lateral dynamics.

Examples of this behavior are present in platforms such as a delta wing, an oblique wing or a hammerhead configuration. The goal of this work was to address these challenges in constructing an aerodynamic model from flight testing. Finally, a note on how to use the proposed flight models for flight control is presented.

6.1 Summary of Contributions

The three main chapters of this thesis contain the primary contributions of this work, reviewed below:

• Chapter 3 presented a supervised learning algorithm to learn UAV flight dy-namics. It showed how the aerodynamic stability and control derivatives can be modeled using dependent Gaussian processes. We performed an in-depth anal-ysis to identify parameters for the highly coupled AD-1 oblique wing aircraft in simulation. The proposed method does not require a prior knowledge of the model structure. We showed how the non-parametric nature of the approach en-abled it to capture a wide range of dynamics compared to a parametric method.

In addition, we demonstrated the advantage of being able to capture dependen-cies through cross coupling terms in the covariance function. It enabled the models to be applicable to a broader flight envelope compared to classical sys-tem identification methods. By not having to know a prior model structure and its ability to capture output correlations, this method can also be effective for the problem of rotorcraft system identification. Furthermore, the model has the inherent capability to handle noise and biased data. We showed its robust-ness to unmodeled disturbances. Likewise, the predictions from the model come with uncertainty estimates, which can be used in maneuver design for system identification and in flight controller design. Finally, the method allows the in-tegration of known knowledge about aircraft dynamics. For instance, the model incorporates existing knowledge about applied forces and moments, such as the output from an engine thrust model and the known structural properties of the platform.

• Chapter 4 extended the dependent Gaussian process model for system identifica-tion in two ways. First by improving its scalability to learn from large test flight data sets and second by capturing non-stationary properties in aerodynamics.

The result is a computationally efficient Gaussian process approximation that combines the best of local and global GPs to model a multi-output system. It uses an additive Gaussian process model that combines both short and long length-scale phenomena for a multi-output GP. By utilizing a combined ap-proximation we were able to learn a broad range of properties in the underlying data. The global GP captures dependencies between outputs and identifies any coupling between parameters. On the other hand, the local GP captures any correlations within those parameters and learns any non-stationary properties.

Most of the desired attributes of the full DGP was retained while reducing the computational cost. The work also introduced a new sampling method for DGPs based on a mutual information criterion. It can sample features that primarily contain information about output correlations. Hence, the model requires less data points to describe a dependent multi-output data set. Finally, this was tested with the AD-1 oblique wing flight simulator. Improvement in learning the model with less number of points was shown in comparison to traditional entropy based sampling.

• Chapter 5 presented experimental results from the algorithms developed in Chapters 3 and 4. A Brumby MkIII UAV was used for collecting the flight data for model training and testing. The hardware requirements which includes specifications of the UAV, its avionics and sensors that were required to col-lect the flight data were presented. The measured input data from the sensors were used as inputs to train the model. The estimation capability of the full DGP model was first tested by comparing the predicted values to the measured response. A comparison was also performed here to show any improvements against the least squares estimator. Next, the results from local and global GP approximation algorithm were presented. Analysis of the results was per-formed by comparing the measured response to the response generated by using

only the global approximation technique. In addition, it was presented how the learned coefficient estimates can be transformed into system states.